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Find the products first. You have to distribute them.
i need help on how to compare and contrast, brb gotta eat @ttnvnusa
Well, if you did the FOIL multiplication of each, what did you get? There should be an obvious difference between them.
uhh so why would they say there is a difference? so why compare and contrast
Did you FOIL them? What are the products? Start there.
Yes,like I said, there is a very obvious difference.
who doesnt understand?
florida virtual school
i dont think its wrong
There is a difference. If you did the FOIL you should see the difference. If you tell me what you got for the products, I can help you from there.
how old are you... you can't spell lol no offense
Or, if not, I'll just move on.
i did foil.... x^2 - 12x + 36 @DebbieG
yes ***(BECAUSE)*** i'm the dumb one.. you can't spell to save your life
ok, that's right for one of them. What about the other one?
And which one did you get that ^^ result for?
the second one @DebbieG
OK, good, now what about the first one? What did you get for that one?
the first one is .. x^2+12+36 @DebbieG
No, try again. It's a "special product". That isn't what you get.
hmmmm cause i have a question bout something i don't know a thing? @vk278 wow
Look at the two binomials, they have a special form. (a - b)(a + b) When you take that product, something "special" happens. Do it carefully, one piece at a time F-O-I-L.
something little people like you wouldn't understand :p @vk278
@DebbieG x^2 - 6x + 6x - 36
OK, good.... now combine those like terms in the middle...
@JOshua_Lewis what do you get when you combine the like terms?
what do you mean? like do they cancel each other out?
Well, you can think of it as "canceling" although I don't really care for that word here. Simply add them together, what do you get??
Just like you added on the other product: you had -6x-6x and got -12x
Hmmm... on this one?? You have: x^2 - 6x + 6x - 36 What is -6x + 6x?
What is -6 + 6?
RIGHT. So what is -6x + 6x???
at first that's why i said "canceled out"
Right, and I said " you can think of it as "canceling" although I don't really care for that word here. Simply add them together, what do you get??" It's more like they offset each other. But if you like to think of it as canceling, that's fine. I didn't mean to mislead you. :)
Exactly! So you have: \((x-6)(x+6)=x^2-36\) And \((x-6)(x-6)=x^2-12x +36\) do you see some differences that you can compare and contrast? About what you end up with, in each case?
IDK how to exactly word it
These are both what are often called "special products".... \((x-6)(x+6)\) is the "product of a sum and a difference" and that always gives you a "difference of squares"... the middle terms of the FOIL will go away, since they "offset" (or cancel :) \((x-6)(x-6)=(x-6)^2\) so that is a "perfect square". It always takes a very specific form (depending on whether the binomial you square is a SUM or a DIFFERENCE): \((x-a)^2=x^2-2ax+a^2\) \((x+a)^2=x^2+2ax+a^2\)
Well, put it in your own words. The key is the difference in how the FOIL product ends up working out. The "magic" in the product of a sum and a difference is the way the middle terms go away, and leave you with a DIFFERENCE OF SQUARES.
well thank you very much! i will for sure come back to you if i have any questions. :)
Sure thing, happy to help! :)